前言
快速上顎擴張為牙科齒列矯正橫向寬度不足的方式之一，常用於治療患者上顎牙弓寬度不足的問題。快速上顎擴張器可分成齒性與骨性兩大類型：骨性快速上顎擴張器是利用骨釘直接傳導力量到上顎骨，從而將上顎骨之顎正中骨縫撐開以增加上顎牙弓寬度；齒性快速上顎擴張器則是將力量直接傳遞到牙齒。研究顯示使用骨性快速上顎擴張器進行治療之患者,其成人可達到較大的橫向(即頰舌側)擴張效果；然而現有針對骨性快速上顎擴張器的相關研究中，大多關注於正中骨縫的擴張位移量，鮮少有研究針對擴張器的結構與患者骨骼和軟組織進行合理的力學評估。因此，本研究之目的是利用臨床影像資料進行結合有限元素法,針對正中骨縫的材料性質與擴張器之幾何設計與植入位置進行力學探討,並以臨床病例之結果加以驗證及比對以提供有效臨床資訊。
材料與方法
本研究利用一位24歲上顎牙弓窄縮男性患者的牙科錐狀斷層掃描影像,經由逆向工程結合電腦輔助繪圖軟體重建患者之三維數位模型,再利用該模型進行有限元素分析。研究共包含兩大部分：(1)利用文獻與患者術後斷層掃瞄影像對有限元素分析模型進行驗證；(2)利用已經由臨床驗證之有限元素模型進一步改變擴張器骨釘的長度與位置來觀察各個設計因子對骨結構、正中骨縫與擴張器的力學反應。在初步的分析設定，本研究建立一個簡單幾何之有限元素模型針對上顎正中骨縫給予不同的彈性係數和普松比，經由調整材料特性參數使其簡單模型的擴張變形結果與臨床相互吻合，進而利用此簡單模型的材料係數設定到患者的有限元素三維模型。之後分別利用長度為9、11和13 mm的市售骨釘植入上顎骨，其擴張器植入位置共有兩處，分別為前側(左右第一小臼齒連線與後側(左右第一大臼齒連線)。在施力條件方面，本研究分別在左右擴張器上給予一個沿著頰舌側方向0.125 mm的位移量，以模擬擴張器旋轉一轉的張開量，其所得之分析結果將再次與臨床資料和文獻進行模型的驗證，並觀察上顎骨與擴張器各部件之位移與應力分布情況，以理解骨性擴張器的力學傳遞機制。
結果
本研究利用文獻與病患資料對簡單有限元素模型進行擴張的變形模式比對，其結果顯示上顎正中骨縫的材料性質會影響上顎撐寬的變形模式，故根據有限元素模型與文獻和臨床資料比對後之結果，在有限元素模型中，上顎正中骨縫的彈性係數設置為0.1 MPa與普松比為0.1；加上周邊上顎骨縫 (翼顎縫Pterygo-palatine、顴顳縫Zygomatico-temporal與顴頷縫Zygomatico-maxillary suture)的彈性係數設置為1370 MPa與普松比0.3時，模型的正中骨縫擴張形式會與臨床結果一致。
後續經臨床驗證過之有限元素模型，在改變不同擴張器的設計因子下，其結果顯示，不同骨釘植入深度和擴張器放置的前後位置並不會影響上顎撐寬的寬度，然而將擴張器放置在上顎骨前側時，擴張器的反作用力會比較該擴張器放置後側時小。本研究之結果可以提供臨床醫師進一步資訊，並且找到上顎擴張器對患者的理想設定，以期許達到最好的撐寬效果。

Introduction
Rapid palatal expansion (RPE) is an orthodontic method for patients with constricted maxilla. Rapid palatal expander is divided into bone-born and tooth-born type types：bone-born expander transmits force to bone screws to further expand maxillary bone；contrarily, tooth-born expander passes on force to tooth directly. Micro-implant assisted RPE, which is one of bone-born expanders, has been proved which could expand the maxilla in adult patients successfully and efficiently. Most of the studies analyzed the effect of various screw position, screw length in micro-implant assisted RME using finite element method (FEM) with different setting of material properties, that contribute to opposite results. Moreover, there are few reports focused on how to create a finite element model and verify the model by clinical results. The purpose of our study is to create a finite element model by changing various suture properties to stimulate the clinical results, and to evaluate the effect of micro-implant assisted RME with verified FEM.
Methods
A finite element model was constructed from a cone beam computed tomography (CBCT) images of a 24 years male. In the first part of study, the effects resulting from different suture property setting was evaluated. The behavior of the FEM was compared with the findings of patient’s clinical result. Comparisons refer to the pattern of suture opening, and reaction force of expander. In second part, using the verified finite element model, two clinical situations with varying screw length (9,11,13) were studied in two 3D models: anterior-positioned between first premolars of both sides and posterior-positioned expander between first molars of both sides. The expander was activated transversely by b 0.125mm of both side of x-axis. Finite element analysis simulations were performed in both 3D models. Deformation and reaction force were evaluated for all models.
Results
The findings of this study suggest that mid-palatal suture’s property play an important role in analysis’s results, identified from the reaction force of expander. It was suggested that practical property of mid-palatal suture was E = 0.1MPa, P=0.1. For other maxillary sutures (Pterygo-palatine, Zygomatico-temporal, Zygomatico-maxillary suture), E = 1370MPa, P=0.3 was recommended, that contribute to rational opening pattern. With the verified model, moreover, changes in screw length and expander position could not affect the width of expansion, but when placing expander anteriorly, reaction force of expander increases much more. A finite element model should be verified by clinical result first, and the results of FEM study would be reliable and applicable to provide more worthy information to clinical doctors.

1. Brunelle JA, Bhat M, Lipton JA. Prevalence and distribution of selected occlusal characteristics in the US population, 1988-1991. J Dent Res. 1996;75(SPEC. ISS.):706–13. doi:10.1177/002203459607502s10
2. DaSilva Filho OG, Santamaria M, Capelozza Filho L. Epidemiology of posterior crossbite in the primary dentition. J Clin Pediatr Dent. 2007;32(1):73-78. doi:10.17796/jcpd.32.1.h53g027713432102
3. Egermark-ErikssonI, Carlsson GE, Magnusson T, Thilander B. A longitudinal study on malocclusion in relation to signs and symptoms of cranio-mandibular disorders in children and adolescents. Eur J Orthod. 1990;12(4):399-407. doi:10.1093/ejo/12.4.399
4. Kutin G, Hawes RR. Posterior cross-bites in the deciduous and mixed dentitions. Am J Orthod. 1969;56(5):491-504. doi:10.1016/0002-9416(69)90210-3
5. Garib DG, Henriques JFC, Janson G, Freitas MR, Coelho RA. Rapid maxillary expansion - Tooth tissue-borne versus tooth-borne expanders: A computed tomography evaluation of dentoskeletal effects. Angle Orthod. 2005;75(4):548-557. doi:10.1043/0003-3219(2005)75[548:RMETVT]2.0.CO;2
6. Gurel HG, Memili B, Erkan M, Sukurica Y. Long-term effects of rapid maxillary expansion followed by fixed appliances. Angle Orthod. 2010;80(1):5-9. doi:10.2319/011209-22.1
7. Zhou Y, Long H, Ye N. The effectiveness of non-surgical maxillary expansion: A meta-analysis. Eur J Orthod. 2014;36(2):233-242. doi:10.1093/ejo/cjt044
8. Ronald B. A review of maxillary expansion in relation to rate of expansion and patient’s age. Am J Orthod. 1982;81(1):32-37.
9. Bazargani F, Feldmann I, Bondemark L. Three-dimensional analysis of effects of rapid maxillary expansion on facial sutures and bones A systematic review. Angle Orthod. 2013;83(6):1074-1082. doi:10.2319/020413-103.1
10. Kokich VG. Age changes in the human frontozygomatic suture from 20 to 95 years. Am J Orthod. 1976;69(4):411-430. doi:10.1016/0002-9416(76)90209-8
11. Harzer W, Schneider M, Gedrange T, Tausche E. Direct Bone Placement of the Hyrax Fixation Screw for Surgically Assisted Rapid Palatal Expansion (SARPE). J Oral Maxillofac Surg. 2006;64(8):1313-1317. doi:10.1016/j.joms.2005.11.061
12. Tausche E, Hansen L, Hietschold V, Lagravère MO, Harzer W. Three-dimensional evaluation of surgically assisted implant bone-borne rapid maxillary expansion: A pilot study. Am J Orthod Dentofac Orthop. 2007;131(4 SUPPL.):92-99. doi:10.1016/j.ajodo.2006.07.021
13. Baysal A, Karadede I, Hekimoglu S. Evaluation of root resorption following rapid maxillary expansion using cone-beam computed tomography. Angle Orthod. 2012;82(3):488-494. doi:10.2319/060411-367.1
14. Halicioǧlu K, Kiki A, Yavuz I. Maxillary expansion with the memory screw: A preliminary investigation. Korean J Orthod. 2012;42(2):73-79. doi:10.4041/kjod.2012.42.2.73
15. Shetty V, Caridad J, Caputo AA, Chaconas SJ. Biomechanical rationale for surgical-orthodontic expansion of the adult maxilla. J Oral Maxillofac Surg. 1994;52(7):742-749. doi:10.1016/0278-2391(94)90492-8
16. Byloff FK, Mossaz CF. Skeletal and dental changes following surgically assisted rapid palatal expansion. Eur J Orthod. 2004;26(4):403-409. doi:10.1093/ejo/26.4.403
17. Gauthier C, Voyer R, Paquette M, Rompré P, Papadakis A. Periodontal effects of surgically assisted rapid palatal expansion evaluated clinically and with cone-beam computerized tomography: 6-month preliminary results. Am J Orthod Dentofac Orthop. 2011;139(4 SUPPL.):16-19. doi:10.1016/j.ajodo.2010.06.022
18. Angelieri F, Cevidanes L HS, Franchi L, Gonçalves JR, Benavides E, McNamara JA. Midpalatal suture maturation: Classification method for individual assessment before rapid maxillary expansion. Am J Orthod Dentofac Orthop. 2013;144(5):759-769. doi:10.1016/j.ajodo.2013.04.022
19. Lee HK, Bayome M, Ahn CS. Stress distribution and displacement by different bone-borne palatal expanders with micro-implants: A three-dimensional finite-element analysis. Eur J Orthod. 2014;36(5):531-540. doi:10.1093/ejo/cjs063
20. Yoon S, Lee DY, Jung SK. Influence of changing various parameters in miniscrew-assisted rapid palatal expansion: A three-dimensional finite element analysis. Korean J Orthod. 2019;49(3):150-160. doi:10.4041/kjod.2019.49.3.150
21. Ghoneima A, Abdel-Fattah E, Hartsfield J, El-Bedwehi A, Kamel A, Kula K. Effects of rapid maxillary expansion on the cranial and circummaxillary sutures. Am J Orthod Dentofac Orthop. 2011;140(4):510-519. doi:10.1016/j.ajodo.2010.10.024
22. Moon W. Class III treatment by combining facemask (FM) and maxillary skeletal expander (MSE). Semin Orthod. 2018;24(1):95-107. doi:10.1053/j.sodo.2018.01.009
23. Romanyk DL, Collins CR, Lagravere MO, Toogood RW, Major PW, Carey JP. Role of the midpalatal suture in FEA simulations of maxillary expansion treatment for adolescents: A review. Int Orthod. 2013;11(2):119-138. doi:10.1016/j.ortho.2013.02.001
24. Latham RA. The development, structure and growth pattern of the human mid-palatal suture. J Anat. 1971;108(1):31-41.
25. Wehrbein H, Yildizhan F. The mid-palatal suture in young adults. A radiological-histological investigation. Eur J Orthod. 2001;23(2):105-114. doi:10.1093/ejo/23.2.105
26. Thilander B, Persson M. Palatal suture closure in man from 15 to 35 Years of Age. Am J Orthod Dentofac Orthop.: 1977;72(1):42-52.
27. Ladewig V de M, Capelozza-Filho L, Almeida-Pedrin RR, Guedes FP, deAlmeida Cardoso M, deCastro Ferreira Conti AC. Tomographic evaluation of the maturation stage of the midpalatal suture in postadolescents. Am J Orthod Dentofac Orthop. 2018;153(6):818-824. doi:10.1016/j.ajodo.2017.09.019
28. Baccetti T, Franchi L, Cameron CG, McNamara JA. Treatment Timing for Rapid Maxillary Expansion. Angle Orthod. 2001;71(5):343-350. doi:10.1043/0003-3219(2001)071<0343:TTFRME>2.0.CO;2
29. Starnbach H, Bayne D, Cleall J, Subtelny JD. Facioskeletal and dental changes resulting from rapid maxillary expansion. Angle Orthod. 1966;36(2):152-164.doi:10.1043/0003-3219(1966)036<0152:FADCRF>2.0.CO;2
30. Garrett BJ, Caruso JM, Rungcharassaeng K, Farrage JR, Kim JS, Taylor GD. Skeletal effects to the maxilla after rapid maxillary expansion assessed with cone-beam computed tomography. Am J Orthod Dentofac Orthop. 2008;134(1):8.e1-8.e11. doi:10.1016/j.ajodo.2007.11.024
31. Cantarella D, Dominguez-Mompell R, Moschik C. Midfacial changes in the coronal plane induced by microimplant-supported skeletal expander, studied with cone-beam computed tomography images. Am J Orthod Dentofac Orthop. 2018;154(3):337-345. doi:10.1016/j.ajodo.2017.11.033
32. Song KT, Park JH, Moon W, Chae JM, Kang KH. Three-dimensional changes of the zygomaticomaxillary complex after mini-implant assisted rapid maxillary expansion. Am J Orthod Dentofac Orthop. 2019;156(5):653-662. doi:10.1016/j.ajodo.2018.11.019
33. Cantarella D, Dominguez-Mompell R, Moschik C. Zygomaticomaxillary modifications in the horizontal plane induced by micro-implant-supported skeletal expander, analyzed with CBCT images. Prog Orthod. 2018;19(1). doi:10.1186/s40510-018-0240-2
34. Aziz T, Ansari K, Lagravere MO, Major MP, Flores-Mir C. Effect of non-surgical maxillary expansion on the nasal septum deviation: a systematic review. Prog Orthod. 2015;16(1). doi:10.1186/s40510-015-0084-y
35. Lee RJ, Moon W, Hong C. Effects of monocortical and bicortical mini-implant anchorage on bone-borne palatal expansion using finite element analysis. Am J Orthod Dentofac Orthop. 2017;151(5):887-897. doi:10.1016/j.ajodo.2016.10.025
36. Robert J. Issacson AHI. Forces poduced by rapid maxillary expansion. University of Minnesota Dental Foundation 1964;34(4).
37. Li N, Sun W, Li Q, Dong W, Martin D, Guo J. Skeletal effects of monocortical and bicortical mini-implant anchorage on maxillary expansion using cone-beam computed tomography in young adults. Am J Orthod Dentofac Orthop. 2020;157(5):651-661. doi:10.1016/j.ajodo.2019.05.021
38. Gautam P, Valiathan A, Adhikari R. Stress and displacement patterns in the craniofacial skeleton with rapid maxillary expansion: A finite element method study. Am J Orthod Dentofac Orthop. 2007;132(1):5.e1-5.e11. doi:10.1016/j.ajodo.2006.09.044